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Mirrors > Home > MPE Home > Th. List > 0lt1o | Structured version Visualization version Unicode version |
Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.) |
Ref | Expression |
---|---|
0lt1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . 2 | |
2 | el1o 7579 | . 2 | |
3 | 1, 2 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 c0 3915 c1o 7553 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-un 3579 df-nul 3916 df-sn 4178 df-suc 5729 df-1o 7560 |
This theorem is referenced by: dif20el 7585 oe1m 7625 oen0 7666 oeoa 7677 oeoe 7679 isfin4-3 9137 fin1a2lem4 9225 1lt2pi 9727 indpi 9729 sadcp1 15177 vr1cl2 19563 fvcoe1 19577 vr1cl 19587 subrgvr1cl 19632 coe1mul2lem1 19637 coe1tm 19643 ply1coe 19666 evl1var 19700 evls1var 19702 xkofvcn 21487 pw2f1ocnv 37604 wepwsolem 37612 |
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